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Self-similar solutions of semilinear wave equations with a focusing nonlinearity

Piotr Bizoń1, Dieter Maison2 and Arthur Wasserman3

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Recommended by F Merle

We prove that in three space dimensions a nonlinear wave equation utt − Δu = up, with p≥ 7 being an odd integer, has a countable family of regular spherically symmetric self-similar solutions.


PACS

02.30.Jr Partial differential equations

MSC

35Bxx Qualitative properties of solutions

35L05 Wave equation

Subjects

Mathematical physics

Dates

Issue 9 (September 2007)

Received 6 February 2007, in final form 4 July 2007

Published 25 July 2007



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